Start-Tv: A Closed-Form Initialization For Total Variation Models

Although there are many iterative solvers for total variation models, few attention has been paid on the fast and effective approximation to their optimal solutions. In this paper, we propose a closed-form filter that can efficiently and effectively approximate the optimal solution of total variation models. This filter has linear computation complexity $O(n)$ with respect to the total number of pixels and constant computation complexity $O(1)$ with respect to the window radius. Taking such filter as an initialization, our method can significantly accelerate all previous iterative solvers. Numerical experiments confirms that our initialization is roughly equivalent to $\mathbf{5 0}$ iterations in the iterative method but $\mathbf{1 0} \times$ faster. The proposed method can be applied in all total variation models to accelerate the optimization process, such as image smoothing, image reconstruction and optical flow estimation.